The rod B is confined to move in the circular groove and is

The rod B is confined to move in the circular groove and is forced into molion by the slotted guide A. When the rod is in the position shown, the magni- tudes of its velocity and acceleration are 12 in./sec and 8 in./sec respectively. Knowing that the slotted guide A is moving up the plane, determine the velocity and acceleration of A at the instant shown. 20 in. 30

Solution

There is the rod A with 30^o to the horizontal. Let us build our cartesian co-ordinate system along it with X-axis along the direction of motion and Y-axis perpendicular to the direction of motion.

We know that with respect to the new co-ordinate axis, the angle of the point B made with X-axis is 30^o

It is also a known fact that the instantaneous direction of a motion subdued by a body in circular motion is always in the direction of the tangent to the circle.

Since the tangent at a point is perpendicular to the line through the point passing through the center, the angle made by the instantaneous velocity with the X-axis of our new co-ordinate system is 60^o

SInce velocity of the point B is 12 in./sec², the velocity of the point B in the X-direction is 8 cos 60^o = 4 in/sec

Hence the body A moves in the X-direction with the velocity of 4 inch/sec

Similarly, the acceleration of A is 8 cos 60^o = 4 inch/sec²